ABSTRACT We take advantage of the largest high‐resolution simulation of cosmic structure growth ever carried out – the Millennium Simulation of the concordance Λ cold dark matter (CDM) cosmogony – to study how the star formation histories, ages and metallicities of elliptical galaxies depend on environment and on stellar mass. We concentrate on a galaxy formation model which is tuned to fit the joint luminosity/colour/morphology distribution of low‐redshift galaxies. Massive ellipticals in this model have higher metal abundances, older luminosity‐weighted ages and shorter star formation time‐scales, but lower assembly redshifts, than less massive systems. Within clusters the typical masses, ages and metal abundances of ellipticals are predicted to decrease, on average, with increasing distance from the cluster centre. We also quantify the effective number of progenitors of ellipticals as a function of present stellar mass, finding typical numbers below two for M* < 1011 M⊙, rising to approximately five for the most massive systems. These findings are consistent with recent observational results that suggest ‘down‐sizing’ or ‘antihierarchical’ behaviour for the star formation history of the elliptical galaxy population, despite the fact that our model includes all the standard elements of hierarchical galaxy formation and is implemented on the standard, ΛCDM cosmogony.